How would the cigarette lighter work? In every BMW I have owned the cigarette lighter is disconnected from the electrical system when the car is off.

P.S. Do yourself a favor and heed TJPark01's advice:

The number of people who will buy a $50-$70K automobile, throw in a cheap Walmart battery and totally ignore the manufacturer's advice to register the battery to the charging software that regulates the charging system in the car amazes me.

Not sure on the E60, but my E38 rear console lighter always has power to it. In fact, that is where my BMW tender connects to maintain the battery. BMW recommends not using this particular tender on the E60, due to the complexity of the electronics.